ABCD is a parallelogram Question is (Pink Area)/(All area)=? (Ratio)

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ABCD is a parallelogram Question is (Pink Area)/(All area)=? (Ratio)

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Answer 1 · 2018-06-02T04:10:01

$E) 18$ $E)" " 18$

Explanation:

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Let $| A B C |$ $|ABC|$ denote area of $A B C$ $ABC$ ,
let $| A B C D | = 18 a, \Rightarrow | A B D | = \frac{18 a}{2} = 9 a$ $color(red)(|ABCD|=18a), => |ABD|=(18a)/2=9a$ ,
as $D E : D A = 1 : 3, \Rightarrow | E B D | = \frac{1}{3} \cdot | A B D | = \frac{1}{3} \cdot 9 a = 3 a$ $DE:DA=1:3, => |EBD|=1/3*|ABD|=1/3*9a=3a$
$\Rightarrow | E B K D | = 2 \cdot | E B D | = 2 \cdot 3 a = 6 a$ $=> color(red)(|EBKD|)=2*|EBD|=2*3a=color(red)(6a)$
Now, draw lines $E M and K Q$ $EM and KQ$ , parallel to $A L and F C$ $AL and FC$ , as shown in the figure.
$=> DeltaDEM and DeltaDAN$ are similar,
$=> DE:EA=DM:MN=1:2$ ,
let $DM=w, => MN=2w$ ,
similarly, $BQ=w, KP=2w$
$DeltaDNL and DeltaDPC$ are similar,
$=> DL:LC=DN:NP=3:1$
as $DN=3w, => NP=w$
$=> "shaded area"=1/6*|EBKD|=1/6*6a=a$
Hence, $|"shaded area"|/|ABCD|=a/(18a)=1/18$

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ABCD is a parallelogram Question is (Pink Area)/(All area)=? (Ratio)

1 Answer

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